Duality of random matrix theory and its application

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400414
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Okinawa Institute of Science and Technology Graduate University
• Principal Investigator: Hikami Shinobu 沖縄科学技術大学院大学, 数理理論物理学, 教授 (30093298)
• Co-Investigator(Kenkyū-buntansha): Kikkawa Ayumi 沖縄科学技術大学院大学, 数理理論物理学ユニット, 研究員 (30572341)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: ランダム行列 / リーマン面 / トポロジー

Outline of Final Research Achievements

By the use of duality theorem of random matrix theory with external source, the method of the evaluation of topological invariants in moduli spaces is developed. The intersection numbers of p-spin curves of moduli spaces are evaluated explicitly, and they are compared with Euler characteristics of Abelianvarieties
. The non-orientable surface also is investigated and intersection numbers, Euler characteristics are obtained.
For the applications to DNA or RNA distribution problem, Gaussian means of random matrix theory is considered as biological applications.

Free Research Field

統計力学